The public, including a sizeable majority of Lib Dem supporters, want far stricter controls on immigration to the UK, according to a poll released last night.

The YouGov survey found 81 per cent support for the government’s cap on economic migration – which will slash the number of non-EU workers given visas by a fifth.

It is part of a policy to cut net migration – the number of people arriving in Britain, versus those leaving – from 215,000 to the ‘tens of thousands’.

However, the public, including a large chunk of Lib Dem supporters, is calling on the Coalition to go much further.

Some 70 per cent of the public thought that net immigration of 50,000 or less would be ‘best for Britain’.

This was the view of 61 per cent of Lib Dems. The figure will surprise party managers, who had widely assumed their supporters wanted relaxed immigration controls.

During the consultation over the government’s cap on economic migrants, Business Secretary Vince Cable repeatedly complained the Home Office was intending to be too tough.

The party is also known to be unhappy with David Cameron’s ‘tens of thousands’ pledge, which did not appear in the Coalition agreement.

But the survey, carried out for Migrationwatch, found 16 per cent of Lib Dems want net migration of 50,000-a-year, and a further 36 per cent want no net immigration – which means the same number of people arriving each years as leaving.

A further nine per cent said there should be more emigrants than immigrants. Overall, this is the view of 19 per cent of the population.

In terms of the cap policy, there was 79 per cent approval by the Lib Dems, compared to 95 per cent of Conservatives and 69 per cent of Labour voters.

The figures will be useful in continuing negotations between the Tories and Lib Dems over cracking down on other routes into the UK, such as marriage and student visas.

Worry: The survey also found public concern about a report warning that white Britons will be a minority by 2066 if immigration continues at the current rate.

Separately, the YouGov survey found public concern about a report, published by an Oxford University academic, warning that white Britons will be a minority by 2066 if immigration continues at the current rate.

Prof David Coleman said that, If immigration stays at its long-term rate of around 180,000 a year, the white British-born population would decline from 80 per cent of the total now to 59 per cent in 2051.

By then white immigrants would have more than doubled from 4 to 10 per cent of the total, while the ethnic minority population would have risen from 16 to 31 per cent.

If the trend continued, the white British population, defined as English, Welsh, Scottish and Irish-born citizens, would become the minority after about 2066, Prof Coleman said.

The poll found that 73 per cent of the public would feel ‘unhappy’ if this scenario proved accurate.

Not so keen: Labour want caps on migration the least of all three parties.

Some 85 per cent of Tory voters held this view, compared to 67 per cent of Labour supporters and 55 per cent of Lib Dems.

A fifth of the public said they would be neither happy nor unhappy.

Sir Andrew Green, chairman of Migrationwatch, said: ‘These results are a strong vote of confidence in the government’s recent measures to control economic migration.

‘But they are also warning that the public, who would like to see even lower levels of immigration, are very unhappy about the long-term consequences of immigration for the make-up of our society. ‘

Last week, Home Office ministers announced a 21,700 cap on visas for workers from outside Europe – a reduction of 20 per cent.

They also promised sharp reduction in the number of student visas being handed out – with most applicants for non-degree courses being rejected.

Figures released by the Office for national Statistics, two days after the announcement, showed the scale of the task facing the government.

In the year to March 2010, net migration was 215,000.

Some 580,000 people moved to Britain, including a record 211,000 students. In the same period 364,000 left the country – the lowest level in a decade.

The net migration totals for 2008 and 2009 were 163,000 and 198,000 respectively.

The Office for National Statistics has said that the population will hit 70million by 2029 if net migration runs at 180,000 a year.